A puzzle in $bar{B}_{(s)}^0 to D_{(s)}^{(*)+} lbrace pi^-, K^-rbrace$ decays and extraction of the $f_s/f_d$ fragmentation fraction

We provide updated predictions for the hadronic decays $bar{B}_s^0to D_s^{(*)+} pi^-$ and $bar{B}^0to D^{(*)+} K^-$. They are based on $mathcal{O}(alpha_s^2)$ results for the QCD factorization amplitudes at leading power and on recent results for the $bar{B}_{(s)} to D_{(s)}^{(*)}$ form factors up to order ${cal O}(Lambda_{rm QCD}^2/m_c^2)$ in the heavy-quark expansion. We give quantitative estimates of the matrix elements entering the hadronic decay amplitudes at order ${cal O}(Lambda_{rm QCD}/m_b)$ for the first time. Our results are very precise, and uncover a substantial discrepancy between the theory predictions and the experimental measurements. We explore two possibilities for this discrepancy: non-factorizable contributions larger than predicted by the QCD factorization power counting, and contributions beyond the Standard Model. We determine the $f_s/f_d$ fragmentation fraction for the CDF, D0 and LHCb experiments for both scenarios.